Mechanism for a Chemical Potential of Nonequilibrium Magnons in Parametric Parallel Pumping

We demonstrate how a magnon chemical potential is generated in parametric parallel pumping. We study how a time-periodic magnetic field of this pumping affects magnon properties of a ferrimagnet in a nonequilibrium steady state. We show that the magnon distribution function of our nonequilibrium steady state becomes the Bose distribution function with $\mu=\omega_{\textrm{p}}/2$, where $\mu$ is the magnon chemical potential and $\omega_{\textrm{p}}$ is the pumping frequency. This result is distinct from the absence of the magnon chemical potential in the standard theory and can qualitatively explain its generation in experiments. We believe our result is a first theoretical demonstration of the generation of the magnon chemical potential in the parametric parallel pumping, providing an important step towards a thorough understanding of properties of nonequilibrium magnons.